DC mode (continuous beam)

Pre-RFQ Low-Energy Beam Transports (LEBTs) operate on a continuous, unbunched beam — there's no longitudinal structure yet. HELIX has DC-aware code paths in both the envelope and multi-particle solvers to handle this regime correctly.

TL;DR

For any pre-RFQ run:

from linac_gen.core.config import BeamConfig

beam_cfg = BeamConfig(
    species="H-",
    energy=0.030,            # 30 keV LEBT exit
    frequency=162.5,         # downstream RFQ frequency (used for unit conversions)
    current=5.0,
    n_particles=20_000,
    distribution="gaussian", cutoff=4.0,
    emit_nx=0.20, emit_ny=0.20,
    alpha_x=0.0, beta_x=0.10,
    alpha_y=0.0, beta_y=0.10,
    emit_z=0.0,              # no longitudinal structure
    alpha_z=0.0, beta_z=1.0,
    continuous=True,         # ← critical
    dc_energy_spread_keV=0.0,
)

The continuous=True flag triggers DC-aware behaviour throughout the simulator:

• The longitudinal coordinate is uniformly sampled over one RF period during particle generation (so SC averaging is correct).
• The PIC solver switches to its 2-D analytic / Bassetti-Erskine / 2-D PIC kick (per dc_kernel).
• The recorder marks each step with continuous_at[i] = True so consumers know σ_φ / σ_W / ε_z are not physically meaningful.

Choosing a DC kernel

SpaceChargeConfig.dc_kernel selects the 2-D transverse kick model:

dc_kernel	Field model	Speed	Use when
"uniform"	analytic linear uniform-elliptical kick	fastest	matching, fast scans, default
"gaussian"	Bassetti-Erskine field of a 2-D Gaussian	medium	rigid-σ MP, per-particle non-linearity
"pic2d"	2-D Hockney FFT PIC over actual particle distribution	slowest	most accurate; analogue of TraceWin's PICNIC_2D

from linac_gen.core.config import SpaceChargeConfig

sc = SpaceChargeConfig(
    dc_kernel="gaussian",   # or "uniform" / "pic2d"
)

Common gotchas

Forget continuous=True and your LEBT explodes

If you forget to set this for a pre-RFQ LEBT, HELIX assumes the beam is bunched and imposes a non-physical longitudinal structure. σ_φ blows up, ε_z grows. Symptoms: looks like SC physics is wrong, but it's just a flag.

PXIE LEBT needs Ki=1 + envelope continuous=True

Two silent failure modes: 1. The PXIE LEBT field maps have Ki=1 (full SC compensation). Forgetting this gives the wrong forces. 2. The envelope solver also needs continuous=True to skip longitudinal SC. Both together: PXIE LEBT mean error 6.93% → 0.84%.

DC-aware envelope solver

The Sacherer ODE (linac_gen.tracking.sacherer) is the DC envelope counterpart. It solves the continuous-beam envelope ODE:

\[ \sigma_x'' + \kappa_x(s)\,\sigma_x - \frac{\varepsilon_x^2}{\sigma_x^3} - \frac{2K}{\sigma_x + \sigma_y} = 0 \]

(and similarly for y) with generalised perveance K = qI / (2π ε₀ m c³ (βγ)³). Scope: drifts, hard-edge quadrupoles, 1-D / 3-D solenoid field maps. No acceleration.

from linac_gen.core.lattice import Lattice
from linac_gen.core.particle import H_MINUS
from linac_gen.core.reference import ReferenceParticle
from linac_gen.elements.drift import Drift
from linac_gen.elements.solenoid import Solenoid
from linac_gen.tracking.sacherer import SachererSolver

# LEBT-style solenoid transport line:
lattice = Lattice()
lattice.add(Drift(name="D1", length=200.0))
lattice.add(Solenoid(name="SOL1", length=300.0, field=0.20))
lattice.add(Drift(name="D2", length=400.0))

ref = ReferenceParticle(species=H_MINUS, w_kin=0.033, frequency=162.5)
bg = ref.bg
initial_twiss = dict(emit_x=0.20 / bg, alpha_x=0.0, beta_x=0.5,
                     emit_y=0.20 / bg, alpha_y=0.0, beta_y=0.5)

solver = SachererSolver(lattice, ref, initial_twiss, current=5.0)
res = solver.run()

Cross-references

• Models — model decision tree.
• Tracking modes → DC modes.
• Worked example: DC LEBT.

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